Quasinormal modes of Reissner-Nordström-AdS black holes under physical field-vanishing boundary conditions

TL;DR

This work addresses the boundary-condition problem for coupled gravitational and electromagnetic perturbations of RN–AdS black holes within AdS/CFT. By introducing a physical field-vanishing (PFV) boundary condition and employing master-function reconstruction, the authors map PFV to explicit boundary conditions: Dirichlet for odd-parity and Robin for even-parity master functions, enabling stable computation of quasinormal modes under these multifield constraints. The study uncovers charge-induced spectral features, including multiple purely imaginary branches and altered overtone bifurcations, and demonstrates that the PFV framework naturally extends to other multifield AdS perturbations. The results provide a practical, gauge-consistent route to boundary conditions in AdS for coupled systems and lay groundwork for nonlinear and higher-order perturbation analyses with potential holographic applications.

Abstract

Boundary conditions play a key role in determining the perturbation behavior of a black hole. Motivated by two guiding principles for single-field perturbations -- the non-deformation of the boundary metric and the vanishing of electromagnetic energy flux at the AdS boundary -- we impose a boundary condition for Reissner-Nordström-AdS (RN-AdS) black holes requiring both the metric and electromagnetic field-strength perturbations to vanish at the AdS boundary, which we term the physical field-vanishing (PFV) condition. Using the formulas for perturbation reconstruction, we translate the PFV condition into boundary conditions on the master functions: Dirichlet-type for odd-parity modes and Robin-type for even-parity modes. With these boundary conditions, we compute the quasinormal frequencies of RN-AdS black holes and identify new spectral features. The PFV prescription introduced here could be applied to other multifield perturbation systems in asymptotically AdS spacetimes.

Figures (3)

• Figure 1: Left, the two lowest purely imaginary-frequency modes of master function $\Psi^{\rm odd}_0$ for $r_+=1,10,50$. Right, purely imaginary-frequency modes of the master function $\Psi^{\rm even}_0$ for $r_+=1.0$.
• Figure 2: Quasinormal frequencies of the master function $\Psi^{\rm odd}_1$. Left panel: frequencies for $r_+=5,10,20$ at overtone $n=1$. Right panel: frequencies for $r_+=50$ at overtones $n=1,2,3$.
• Figure 3: The real (left) and imaginary (right) parts of quasinormal frequencies computed from master function $\Psi^{\rm even}_1$ at $r_+=10$ and overtones $n=1,2,3$. The connectivity between $n=1$ and $n=2$ is evident when both modes are purely imaginary.